Method for full-digital random sampling

ABSTRACT

For the signal under acquisition which varies monotonically before and after the trigger time, a method for full-digital random sampling employs first sampled data before the trigger time and first sampled data after the trigger time to fit a curve, and obtains an intersection point of triggering level and the fitted curve, then, calculates the time interval between sampled data after the trigger time and the intersection point in the end, reconstructs the original signal, i.e. the signal under acquisition by a time interval of each acquisition. Thus, an analog trigger circuit and a time measurement circuit of conventional random sampling system can be eliminated, that simplifies the circuit design of data acquisition system and decreases its hardware complexity. Moreover, the higher sampling rate for the signal under acquisition is attained, and more waveform details are obtained.

FIELD OF THE INVENTION

This application claims priority under the Paris Convention to ChinesePatent Application No. 201410692582.4. Filed Nov. 26, 2014, the entiretyof which is hereby incorporated by reference for all purposes as iffully set forth herein.

The present invention relates to the field of data acquisition, moreparticularly to a method for full-digital random sampling.

BACKGROUND OF THE INVENTION

Data acquisition technology have been widely applied to various fields,such as electronic measurement, communication, radar, aerospace andindustry. With the development of technology and engineeringapplication, the complexity of application system increases, and thefrequency of the signal under acquisition (a continuous-time andcontinuous-amplitude analog signal, also called as input signal of DAS)is much higher than ever, that demands data acquisition system to raiseits sampling rate. However, subject to the performance ofanalog-to-digital converter (ADC), it is rather difficult todramatically enhance the real-time sampling rate of data acquisitionsystem (DAS) to acquire enough waveform information of the signal underacquisition, some waveform information of the signal under acquisitionwill be lost, leading to the distortion of reconstructed signal. Tosolve the problem of the distortion of reconstructed signal, randomsampling is employed to obtain ultrahigh sampling rate waveforminformation of periodic signal through multiple sampling.

Random sampling, belonging to non-real-time sampling, is an equivalentsampling, which uses the randomness of sampling signal relative to thesignal under acquisition and triggering event to obtain high samplingrate through multiple acquisition and data merging. In practice,considering the randomness of the time interval between the trigger timeand the first sampling time after the trigger, Random sampling uses highprecise time interval measurement to obtain the time interval, and thenreconstruct the original signal i.e. the signal under acquisition withhigher sampling rate on basis of the time interval of each acquisition.The process of acquiring, storing and reconstructing of the signal underacquisition is shown in FIG. 1.

As shown in FIG. 1, random sampling employs sampling clock of periodT_(s) (sampling rate of ADC) to acquire the sampled data of the signalunder acquisition multiple times (supposing the number of acquisitiontimes is N), and multiple pluralities of sampled data d_(ij) areobtained, then stored in acquisition normal sequence (acquisitionstorage). Wherein, i is acquisition serial number and j is the sampleddata sequence number. After the acquisition storage, there isreconstruction storage, the i^(th) storage of sampled data is based onthe time interval t_(i) between trigger time Tr_(i) of the i^(th)acquisition and the first sampling time after the trigger of the i^(th)acquisition. The waveform of the original signal, i.e. the signal underacquisition will be reconstructed with sampled data of thereconstruction storage (waveform reconstruction).

Given the measurement resolution is T_(s)/M, equivalent sampling rate ofreconstructed waveform is M times original sample rate, i.e. M/T_(s).That makes the data acquisition system having much higher equivalentsampling rate, and the equivalent sampling rate is irrelevant to thesampling rate of ADC, but concerned only to the measurement accuracy oftime interval t_(i), the higher equivalent sampling rate depends on thehigher measurement accuracy of time interval t_(i).

FIG. 2 is a functional block diagram of the random sampling system inprior art.

The conventional random sampling is realized on the basis of analogcircuits and logic devices. As shown in FIG. 2, the conventional randomsampling system comprises signal conditioning circuit, analog triggerchannel, analog-to-digital converter (ADC), field programmable gatearray (FPGA), digital signal processor (DSP), sampling clock generator,time interval measurement module, etc.

After conditioned by signal conditioning circuit, the signal underacquisition is sampled and quantized by ADC, and then the sampled dataSDATA and synchronous clock DCLK is sent to FPGA. At the same time, thetrigger is also sent from analog trigger channel to the FPGA. Every timewhen acquisition begins, the FPGA opens the writing enable wen to storea section (pre-triggering depth) of pre-triggering sampled data to theFIFO of FPGA, then opens reading enable ren to maintain the volume ofpre-triggering sampled data with pre-triggering depth, waiting fortriggering event. When the triggering event (e.g. rising or falling edgeof the signal under acquisition) comes, the analog trigger channel sendsa trigger signal to FPGA, and then FPGA closes reading enable ren, andgenerates a measurement pulse based on the time interval t_(i) betweentrigger time Tr_(i) of the i^(th) acquisition and the first samplingtime after the trigger of the i^(th) acquisition. The measurement pulseis sent to the time interval measurement module for measuring. When theFIFO of FPGA attains sampled data up to the volume required, anacquisition is accomplished. FPGA closes writing enable wen, andcalculates the corresponding address of the plurality of sampled datafor back-end waveform display according to the result of time intervalof the acquisition. The process of acquisition and time intervalmeasurement is repeated multiple times, and multiple pluralities ofsampled data are obtained. Each plurality of sampled data is storedaccording to the calculated corresponding address. The waveformreconstruction of data acquisition is realized based on stored sampleddata. Considering the frequency irrelevance of the sampling clock andthe signal under acquisition, the sampled data in FIFO can cover alllocations after some time. As shown in lower part of FIG. 1, the signalunder acquisition is completely reconstructed when displayed. Theprocesses mentioned above are regulated by digital signal processor(DSP).

The aforementioned random sampling can solve the problem ofhigh-frequency signal acquisition that cannot meet the Nyquist samplingtheorem, but its hardware circuit is rather complicated. With regard tothe signal under acquisition, which frequency is relatively not muchhigher comparing to the sampling clock, but required more specificwaveform details, the random sampling mentioned above is dispensable.

SUMMARY OF THE INVENTION

The present invention aims to overcome the deficiencies of prior art andprovides a method for full-digital random sampling to decrease thehardware complexity of data acquisition, and realize the dataacquisition of signal with high sampling rate and more waveform details.

To achieve these objectives, in accordance with the present invention, amethod for full-digital random sampling is provided, comprising thefollowing steps:

(1) Random Sampling and Storing

acquiring the sampled data of signal under acquisition by the ADC ofrandom sampling system, wherein, the signal under acquisition variesmonotonically before and after the trigger time, and in the monotonicsection, a sampled data can be obtained before and after the triggertime respectively;

sending the sampling command randomly by controller of data acquisitionsystem to open the writing enable (wen) of the FIFO (First In First Out)for storing sampled data from the ADC;

when pre-triggering depth L_(p) of the FIFO is attained, opening thereading enable (ren) of the FIFO to maintain the volume of sampled datawith depth L_(p); meanwhile, detecting whether the sampled data issatisfied with the triggering condition, once satisfied, closing thereading enable (ren) of the FIFO; and when the storage depth L_(s) of anacquisition is attained, closing the writing enable (wen) of the FIFO;by this moment, the range of sampled data in the FIFO is[d_(n−Lp+1),d_(n+Ls−Lp)], where 1≦L_(p)≦L_(s), the trigger is betweenthe sampled data d_(n) and d_(n+1), where n is the position of the firstsampled data before the trigger and n+1 is the position of the firstsampled data after the trigger,

(2) Curve Fitting and Trigger Relocating

fitting a curve on the basis of sampled data d_(n) and d_(n+1), theintersection point Tr_(L) of triggering level A_(T) and the fitted curvecan be obtained, then calculating the time interval t_(L) betweensampled data d_(n+1) and the intersection point Tr_(L);

(3) Waveform Reconstructing

according to step (1) and step (2), repeating the process of acquisitionand time interval calculation, and multiple pluralities of sampled datad_(ij) and the time interval t_(Li) of each acquisition are obtained,where i is the acquisition serial number, iεN, N is the number ofacquisition, j is sampled data sequence number; then, interlacing themultiple pluralities of sampled data d_(ij) by ascending order of thetime interval t_(Li), and storing the interlaced multiple pluralities ofsampled data d_(ij); in the end, reconstructing the original signal i.e.the signal under acquisition with the interlaced multiple pluralities ofsampled data d_(ij).

The objectives of the present invention are realized as follows:

For the signal under acquisition which varies monotonically before andafter the trigger time, the present invention, i.e. method forfull-digital random sampling employs the first sampled data (d_(n))before the trigger time and the first sampled data (d_(n+1)) after thetrigger time to fit a curve, and obtains a intersection point Tr_(L) oftriggering level A_(T) and the fitted curve, then, calculates the timeinterval t_(L) between sampled data d_(n+1) and the intersection pointTr_(L), in the end, reconstructs the original signal. i.e. the signalunder acquisition by the time interval t_(Li) of each acquisition. Thus,an analog trigger circuit and a rime measurement circuit of conventionalrandom sampling system can be eliminated, that simplifies the circuitdesign of data acquisition system and decreases its hardware complexity.Moreover, the higher sampling rate for the signal under acquisition isattained, and more waveform details are obtained.

BRIEF DESCRIPTION OF THE DRAWING

The above and other objectives, features and advantages of the presentinvention will be more apparent from the following detailed descriptiontaken in conjunction with the accompanying drawings, in which:

FIG. 1 is a diagram of the acquiring, storing and reconstructing of thesignal under acquisition in conventional random sampling;

FIG. 2 is a functional block diagram of conventional random samplingsystem;

FIG. 3 is a functional block diagram of a random sampling system inaccordance with the present invention;

FIG. 4 is a diagram of digital triggering and storage controlling inaccordance with the present invention;

FIG. 5 is a diagram of trigger relocating based on linear fitting inaccordance with the present invention;

FIG. 6 is a diagram of trigger relocating based on sinusoidal fitting inaccordance with the present invention;

FIG. 7 is a diagram of the processing of sampled data (the signal underacquisition is sinusoidal wave) in accordance with the presentinvention;

FIG. 8 is another diagram of the processing of sampled data (the signalunder acquisition is square wave) in accordance with the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Hereinafter, preferred embodiments of the present invention will bedescribed with reference to the accompanying drawings. It should benoted that the similar modules are designated by similar referencenumerals although they are illustrated in different drawings. Also, inthe following description, a detailed description of known functions andconfigurations incorporated herein will be omitted when it may obscurethe subject matter of the present invention.

Random sampling is a method that can enhance equivalent sampling rateeffectively to obtain more details of a periodic signal. It repeatedlyacquires the sampled data of a periodic signal at relatively lowersampling rate according to the irrelevance between the sampling clockand the signal under acquisition, and multiple pluralities of sampleddata and the time interval of each acquisition are obtained. Then, itreconstructs the signal under acquisition with higher equivalentsampling rate according to the ordinal relations of the multiplepluralities of sampled data.

The present invention removes analog triggering channel and timeinterval measurement module from the conventional random samplingsystem, and uses digital signal processing (random sampling and storing,curve fitting and trigger relocating) to determine the ordinal relationof the multiple pluralities of sampled data for waveform reconstructing,in the end, reconstructs the original signal i.e. the signal underacquisition.

FIG. 3 is a functional block diagram of a random sampling system inaccordance with the present invention.

In one embodiment, as shown in FIG. 3, after conditioned by signalconditioning circuit, the signal under acquisition is sampled andquantized by ADC, and then the sampled data SDATA and synchronous clockDCLK is sent to FPGA. The sampled data SDATA is stored and processed inFPGA or DSP, which comprises random sampling and storing, curve fittingand trigger relocating, and waveform reconstructing. Comparing to FIG.1, the random sampling system in accordance with present invention haseliminated the analog trigger channel and time interval measurementmodule. While, a digital trigger controlling module is added before thesampled data storage to generate an effective triggering signal, andcurve fitting and trigger relocating module is added after the sampleddata storage to find the ordinal relation of the multiple pluralities ofsampled data. In the end, the reconstructing of the signal underacquisition can be realized.

In accordance with the present invention, the method for full-digitalrandom sampling comprises the following steps: random sampling andstoring, curve fitting and trigger relocating, and waveformreconstructing.

1. Random Sampling and Storing

Random sampling and storing consists of digital trigger controlling andsampled data storage, digital trigger controlling provides an importantbasis for sampled data storing. The principle of random sampling andstoring is shown in FIG. 4.

In one embodiment of present invention, As the controller of dataacquisition system, DSP sends the sampling command randomly, to open thewriting enable (wen) of the FIFO (First in First Out) for storingsampled data from the ADC.

When pre-triggering depth L_(p) of the FIFO is attained. DSP opens thereading enable (ren) of the FIFO to maintain the volume of sampled datawith depth L_(p); meanwhile, the digital trigger controlling moduledetects whether the sampled data is satisfied with the triggeringcondition. Assuming triggering level is A_(T) and the triggeringcondition is a negative edge, so the criterion that sampled data d_(n)and d_(n+1) is satisfied with the triggering condition is:

d _(n) ≧A _(T), and d _(n+1) <A _(T)  (1).

Similarly the triggering condition is a positive edge, the criterionthat sampled data d_(n) and d_(n+1) is satisfied with the triggeringcondition is:

d _(n) ≦A _(T), and d _(n+1) >A _(T)  (2).

Once satisfied, DSP closes the reading enable (ren) of the FIFO. Andwhen the storage depth L_(s) of an acquisition is attained, DSP closesthe writing enable (wen) of the FIFO. By this moment, the range ofsampled data in the FIFO is [d_(n−Lp+1),d_(n+Ls−Lp)], where1≦L_(p)≦L_(s). As shown in FIG. 4, the triggering condition is anegative edge, after searching and analyzing, the digital triggercontrolling module can find that the trigger is between d₃ and d₄, wheren=3, d₃ is the first sampled data before the trigger, d₄ is the firstsampled data after the trigger, and the range of sampled data in theFIFO is [d_(4−Lp),d_(3+Ls−Lp)].

With the process of random sampling and storing mentioned above, notonly the stored sampled data are satisfied with the storage depth, butalso the preliminary position of trigger is obtained. And that lays thegroundwork for the back end processing of sampled data.

2. Curve Fitting and Trigger Relocating

After the preliminary position of trigger is obtained, the signal underacquisition can be restored as accurately as possible through curvefitting on the basis of sampled data d_(n) and d_(n+1), the moreaccurate position of trigger can be obtained by trigger relocating. Andthat provides the parameter for reconstructing the signal underacquisition with higher equivalent sampling.

The way of curve fitting depends on the specific characteristics of thesignal under acquisition. The common ways involve linear fitting andsinusoidal fitting. As shown in FIG. 5 and FIG. 6. The more accurateposition of trigger in sampled data is obtained through curve fitting onthe basis of the preliminary position of trigger shown in FIG. 4.

FIG. 5 shows a diagram of trigger relocating based on linear fitting.Sampled data d₃ and d₄ are connected by a straight line, a intersectionpoint Tr_(L) of triggering level A_(T) and the straight line, i.e. thefitted curve can be obtained. The time interval t_(L) between sampleddata d₄ and the intersection point Tr_(L) is:

$\begin{matrix}{{t_{L} = {\frac{A_{T} - d_{4}}{d_{3} - d_{4}} \cdot T_{s}}};} & (3)\end{matrix}$

where T_(s) is the sampling period of the ADC.

FIG. 6 shows a diagram of trigger relocating based on sinusoidalfitting. The model function of sinusoidal signal is y=a_(x)sin(2πt/T_(x)+Φ_(x))+A_(x), where a_(x), T_(x), φ_(x), A_(x) and yrepresent amplitude, period, initial phase, DC offset and the amplitudeof time r respectively. According to the model function of sinusoidalsignal a equation is obtained as follows:

d _(j) =a _(x)·sin(2π·t _(j) /T _(x)+φ_(x))+A _(x)  (4);

where d_(j) is the jth sampled data, t_(j) is jth sampling time. Thus afour-parameter sinusoidal fitting problem is obtained. According toparameter estimation method, we can get their estimated values {dot over(a)}_(x), {dot over (T)}_(x), {dot over (φ)}_(x) and {dot over (A)}_(x).Therefore, the waveform expression after sinusoidal curve fitting is:

$\begin{matrix}{y = {{{\hat{a}}_{x} \cdot {\sin ( {{2{\pi \cdot {t/{\hat{T}}_{x}}}} + {\hat{\phi}}_{x}} )}} + {{\hat{A}}_{x}.}}} & (5)\end{matrix}$

And the time of intersection point Tr_(L) is

${t_{T} = {\frac{{\hat{T}}_{x}}{2\; \pi}{\arcsin \lbrack {( {A_{T} - {\hat{A}}_{x}} )/{\hat{a}}_{x}} \rbrack}}},$

thus the time interval t_(L) between sampled data d₄ and theintersection point Tr_(L) is:

$\begin{matrix}{t_{L} = {{{3\; T_{s}} - t_{T}} = {{3\; T_{s}} - {\frac{{\hat{T}}_{x}}{2\; \pi}{{\arcsin \lbrack {( {A_{T} - {\hat{A}}_{x}} )/{\hat{a}}_{x}} \rbrack}.}}}}} & (6)\end{matrix}$

Two kind of curve fitting and trigger relocating based on linear curvefitting and sinusoidal curve fitting are analyzed above. However, inpractice, the ways of curve fitting and trigger relocating are notlimited to the said ways, and different curve fitting mode can beemployed due to different characteristics of signal under acquisition,so as more accurate position of trigger can be obtained.

3. Waveform Reconstructing

Repeating the process of acquisition and time interval calculation, andmultiple pluralities of sampled data d_(ij) and the time interval t_(Li)of each acquisition are obtained. Therefore, we can reconstruct thesignal under acquisition with higher equivalent sampling.

Supposing that equivalent sampling rate of reconstructed signal f_(s) isM times the sampling rate of ADC fs, the time resolution ofreconstructed signal is Δt=T_(s)/M. Meanwhile, the digital triggerinterval is divided into M subintervals [Δt·(k−1),Δt·k), where k=1, 2, .. . , M. Then, the position k_(i) of the i^(th) storage of sampled datameets the condition:

t _(Li) ε[T _(s)·(k _(i)−1)/M,T _(s) ·k _(i) /M)  (7).

For example, if the time interval t_(Li) of i^(th) acquisition satisfiesthe equation (7), then the address of the plurality of sampled data area_(j−M+k) _(i) , which is shown in FIG. 7, where k_(i)=2, i.e. as a setof M successive addresses, the sample data in i^(th) acquisition isstored in the 2^(nd) address and so forth. Therefore, time intervalst_(Li) are sorted by the ascending order so as to interlace andrecombine the data d_(ij) from each acquisition successively.

FIG. 8 shows another diagram of the processing of sampled data. Thesignal under acquisition is square wave. The random sampling is similarto FIG. 7. The sampling rate is enhanced dramatically, and more accuratereconstructed signal is obtained.

After the aforementioned analysis, the key to present invention is theaccuracy of trigger relocating and, in practice, it is determined by theaccuracy of curve fitting. However, the accuracy of curve fitting iscorrelated with the jitter of sampling clock edge. Thus the dataacquisition system needs sampling clock with lower jitter to acquirehigh resolution sampled data.

In the embodiment mentioned above, sinusoidal fitting and linear fittingare employed for trigger relocating, which has a significant effect onenhancing equivalent sampling rate when the signal under acquisitionvaries monotonically near the trigger. With regard to more complicatedsignal under acquisition, we should use more precise curve fittingmethod such as fuzzy matching, neural network, etc to enhance theaccuracy of trigger relocating, in the end, to enhance the equivalentsampling rate.

SUMMARIZATION

The innovation of the present invention lies in: (i) overcoming thedeficiencies of conventional random sampling in prior art byfull-digital processing, i.e. high hardware performance and complicatedstructure; (ii) providing an effective way to relocate the triggerthrough curve fitting. The present invention is now applied only to thesignal which vanes monotonically near the trigger, yet new researchorientation on full-digital random sampling is exploited, and a newpathway on signal feature extraction for data postprocessing isproposed.

While illustrative embodiments of the invention have been describedabove, it is, of course, understand that various modifications will beapparent to those of ordinary skill in the art. Such modifications arewithin the spirit and scope of the invention, which is limited anddefined only by the appended claims.

What is claimed is:
 1. A method a method for full-digital randomsampling is provided, comprising the following steps: (1). randomsampling and storing acquiring the sampled data of signal underacquisition by the ADC of random sampling system, wherein, the signalunder acquisition varies monotonically before and after the triggertime, and in the monotonic section, a sampled data can be obtainedbefore and after the trigger time respectively; sending the samplingcommand randomly by controller of data acquisition system to open thewriting enable (wen) of the FIFO (First In First Out) for storingsampled data from the ADC; when pre-triggering depth L_(p) of the FIFOis attained, opening the reading enable (ren) of the FIFO to maintainthe volume of sampled data with depth L_(p); meanwhile, detectingwhether the sampled data is satisfied with the triggering condition;once satisfied, closing the reading enable (ren) of the FIFO; and whenthe storage depth L_(s) of an acquisition is attained, closing thewriting enable (wen) of the FIFO; by this moment, the range of sampleddata in the FIFO is [d_(n−Lp+1),d_(n+Ls−Lp)], where 1≦L_(p)≦L_(s), thetrigger is between the sampled data d_(n) and d_(n+1), where n is theposition of the first sampled data before the trigger and n+1 is theposition of the first sampled data after the trigger; (2). curve fittingand trigger relocating fitting a curve on the basis of sampled datad_(n) and d_(n+1), the intersection point Tr_(L) of triggering levelA_(T) and the fitted curve can be obtained, then calculating the tuneinterval t_(L) between sampled data d_(n+1) and the intersection pointTr_(L); (3). waveform reconstructing according to step (1) and step (2),repeating the process of acquisition and time interval calculation, andmultiple pluralities of sampled data d_(ij) and the time interval t_(Li)of each acquisition are obtained, where i is the acquisition serialnumber, iεN, N is the number of acquisition, j is sampled data sequencenumber; then, interlacing the multiple pluralities of sampled datad_(ij) by ascending order of the time interval t_(Li), and storing theinterlaced multiple pluralities of sampled data d_(ij); in the end,reconstructing the original signal, i.e. the signal under acquisitionwith the interlaced multiple pluralities of sampled data d_(ij).
 2. Amethod for full-digital random sampling of claim 1, wherein thetriggering level is A_(T), if the triggering condition is a negativeedge, the criterion that sampled data d_(n) and d_(n+1) is satisfiedwith the triggering condition is:d _(n)

A _(T), and d _(n+1) <A _(T); and, if the triggering condition ispositive edge, the criterion that sampled data d_(n) and d_(n+1), issatisfied with the triggering condition is:d _(n)

A _(T), and d _(n+1) >A _(T).
 3. A method for full-digital randomsampling of claim 1, wherein the curve fitting is linear fitting orsinusoidal fitting.